$ -\dfrac{8}{6} \div \left(\dfrac{4}{9} \div -\dfrac{5}{3}\right) = {?} $
Solution: First, we can simplify the problem: $ -\dfrac{4}{3} \div \left(\dfrac{4}{9} \div -\dfrac{5}{3}\right) = {?} $ Dividing by a fraction is the same as multiply by the reciprocal of that fraction. $ = -\dfrac{4}{3} \div \left(\dfrac{4}{9} \times -\dfrac{3}{5}\right) $ $ = -\dfrac{4}{3} \div \left(\dfrac{4 \times -3} {9 \times 5}\right) $ $ = -\dfrac{4}{3} \div -\dfrac{12}{45} $ $ = -\dfrac{4}{3} \times -\dfrac{45}{12} $ $ = \dfrac{-4 \times -45}{3 \times 12} $ $ = \dfrac{180}{36}$ Simplify: $ = 5$